A Garden of Statistically Self-Similar Plants

Anne Burns
Proceedings of Bridges 2009: Mathematics, Music, Art, Architecture, Culture (2009)
Pages 231–238 Regular Papers


A simple fractal tree has the property of self-similarity, meaning it can be subdivided into parts, each of which is a reduced copy of the whole tree; its fractal dimension can be calculated from the scaling factor. Trees in nature exhibit an “approximate self-similarity”. Using discrete time steps and probabilities, an algorithm for drawing plants that are not strictly self-similar, but that appear to belong to the same family, is described. The algorithm is based on a thesis of de Reffye and can be used in artwork and teaching. It has no claim to botanical accuracy, but creates images of purely decorative plants.